Lattice 3-polytopes with few lattice points (Q161310)

In this paper the authors develop an extension of White's theorem on empty tetrahedra. They provide a complete classification of lattice 3-polytopes with five lattice points, showing that, apart from infinitely many of width one, there are exactly nine equivalence classes of them with width two and none of larger width. Additionally the authors prove a general theorem: for every positive integer \(n\) there is only a finite number of (integer congruence classes of) lattice 3-polytopes with \(n\) lattice points and of width larger than one.